Zeta function of self-adjoint operators on surfaces of revolution

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Issue Date
2015-04-10
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Authors
Lu, Tianshi
Jeffres, Thalia D.
Kirsten, Klaus
Advisor
Citation

Lu, Tianshi; Jeffres, Thalia D.; Kirsten, Klaus. 2015. Zeta function of self-adjoint operators on surfaces of revolution. Journal of Physics A: Mathematical and Theoretical, vol. 48:no. 14:Article no. 145204

Abstract

In this article we analyze the zeta function for the Laplace operator on a surface of revolution. A variety of boundary conditions, separated and unseparated, are considered. Formulas for several residues and values of the zeta function as well as for the determinant of the Laplacian are obtained. The analysis is based upon contour integration techniques in combination with a WKB analysis of solutions of related initial value problems.

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